标题： 分圆层次映射和简单仿射顶点代数的相关簇 显示英文标题

标题： Cyclotomic level maps and associated varieties of simple affine vertex algebras

摘要： 在本文中，我们引入并研究了两个分圆层次映射，分别定义在复半单李代数 $\mathfrak{g}$中幂零轨道 $\underline{\mathcal{N}}$的集合以及其Weyl群中的共轭类 $\underline{W}$的集合上，取值为正整数。 我们证明这两个映射在Lusztig的映射 $\underline{W} \to \underline{\mathcal{N}}$下是相容的，该映射也如Yun所展示的那样是极小约化类型映射。 我们还讨论了它们与仿射Weyl群中的双边细胞之间的关系。 我们利用这些映射提出了一个关于非可容纳整数层次下与 $\mathfrak{g}$相关的简单仿射顶点代数的关联簇的猜想，并为此猜想提供了一些证据。 显示英文摘要

摘要： In this paper, we introduce and study two cyclotomic level maps defined respectively on the set of nilpotent orbits $\underline{\mathcal{N}}$ in a complex semi-simple Lie algebra $\mathfrak{g}$ and the set of conjugacy classes $\underline{W}$ in its Weyl group, with values in positive integers. We show that these maps are compatible under Lusztig's map $\underline{W} \to \underline{\mathcal{N}}$, which is also the minimal reduction type map as shown by Yun. We also discuss their relationship with two-sided cells in affine Weyl groups. We use these maps to formulate a conjecture on the associated varieties of simple affine vertex algebras attached to $\mathfrak{g}$ at non-admissible integer levels, and provide some evidence for this conjecture.